Problem: Solve for $x$ and $y$ using substitution. ${x+3y = 5}$ ${y = 2x+11}$
Answer: Since $y$ has already been solved for, substitute $2x+11$ for $y$ in the first equation. ${x + 3}{(2x+11)}{= 5}$ Simplify and solve for $x$ $x+6x + 33 = 5$ $7x+33 = 5$ $7x+33{-33} = 5{-33}$ $7x = -28$ $\dfrac{7x}{{7}} = \dfrac{-28}{{7}}$ ${x = -4}$ Now that you know ${x = -4}$ , plug it back into $\thinspace {y = 2x+11}\thinspace$ to find $y$ ${y = 2}{(-4)}{ + 11}$ $y = -8 + 11$ $y = 3$ You can also plug ${x = -4}$ into $\thinspace {x+3y = 5}\thinspace$ and get the same answer for $y$ : ${(-4)}{ + 3y = 5}$ ${y = 3}$